I finally figured out how to calculate the worst-case minimum required reservoir capacitance for a sine signal at less than the fmains frequency, in the presence of rectifier charging pulses.

There's an interesting table of C values versus frequencies, for each de-rated max output power that could be chosen for a given theoretical max power, in the attached spreadsheet.

You can enter your Rload, Vrail, fmains, etc, and it calculates everything else for you. It basically shows what Rated Max Power you would have, for different capacitances, in order to avoid clipping when operating at the rated max output power.

It ALSO shows the lowest frequency sine your amplifier could reproduce without clipping, for a given reservoir capacitance, when operating at the rated max output power.

I also made an MS Word doc that gives the equations used in the spreadsheet, with partial derivations. (I didn't want to take the time to enter the many equations for all of the steps of the derivations.)

You the man Gotee......... Why can't all of this just be nice and easy..... If you have been reading the Blowtorch thread recently you will see some parallel research into the transformer side of things leaving out the capacitor and only looking at the actions of the tranny. It just keeps getting more complex when you look at each components interaction with the mains currents.

Easy generally means problems that can be resolved by applying well understood concepts. A power supply's pretty much a filter. The impedances and loading are rather different than what's found in things that are usually called filters, but a passive linear supplies we're focusing on here are integrators like any other lowpass filter. One major difference is mainstream filter theory, if you will, assumes a constant load impedance on the filter. This is a pretty good approximation for class A amplifiers, which is why class A loading usually feels like a major simplification in supply design. It's someplace between a poor to awful approximation for class B, D, etc. The other major difference is mainstream filter theory focuses on filters where either both the input and output are continuous time or they're both discrete time (sampled). The bridge diodes mean the supply "filter" essentially has a discrete time input and an continuous time output.

In other words, a power supply is a DAC. In particular, it's a DAC with, by conventional DAC standards, a very noisy and extremely low quality sample and hold circuit into the switched capacitor filter. So not only do you have to think outside the box with respect to filter theory most of the simplifying assumptions that can be made with DACs don't apply to power supplies. A full wave bridge yields a Nyquist rate equal to the mains frequency. This means nearly all of the bandwidth of interest is aliased, something which is studiously avoided in most discrete time systems.

Power supplies would be a lot less fun and challenging if they didn't make you think sideways like this, though. I was running an analysis similar to Tom's for a class AB active triamp I'm working on not too long ago, which throws in some extra twists as you've one channel's worth of audio signal that's split across three different loads to the supply. Since there are three channels rather than one or two there's higher quiescent dissipation and hence a little of the load shifts from class B to class A. If you decide not to ignore this life gets rather interesting since the crossover means all the slow moving portions of the load are assigned to whichever amp is driving the subwoofer. Therefore, the midrange channel pretty much operates above the bridge's switching rate and be treated as an RMS load rather than the almost DC cases which come up in the deep bass for the sub channel. The same applies to a tweeter channel, but its RMS level will be lower due to the mid and sub taking the lower frequencies. So you end up with parameter sweeps over crossover frequency and music power spectral densities as well as the usual mains level and capacitor size variations.

You the man Gotee......... Why can't all of this just be nice and easy..... If you have been reading the Blowtorch thread recently you will see some parallel research into the transformer side of things leaving out the capacitor and only looking at the actions of the tranny. It just keeps getting more complex when you look at each components interaction with the mains currents.

Steven

It looks like everyone who has ever tried to analyze a simple transformer-rectifier-capacitor power supply has found it to be "surprisingly complex", at least mathematically.

One reason I've been playing with this stuff is to try to make it easier for everyone else.

Also, I hope to dispel some myths and head off some common mistakes and misconceptions, so people might have an easier time, and a better chance at getting better results, sooner rather than later.

Just to recap a little:

One of the first important concepts that needs to be emphasized is that the CURRENT is where the action is. The current is the music signal, and is what the power supply is for, and what it needs to be best at providing. The usual "voltage centric" view of the power supply (and of everything else) misses the point and is less likely to lead to a good understanding of what is most important.

It would be nice to also hold the voltage constant but often it's not too critical. Note, too, that ripple voltage is not the periodic sawtooth from the textbooks, unless the load is extremely boring. Ripple voltage is caused by the music current, as it drains the caps between charging pulses from the rectifier, and also as it gets pulled through the rails' inductances (and resistances), since V = L di/dt (and V = iR).

Decoupling caps, like little power supplies right at the point of load, can help stop ripple from even starting, but are also necessary for accurate transient response and feedback operation, especially for the higher-frequency and shorter-duration events. Inductance is our enemy and distance/length means inductance. I would use at least 10 uF per Watt, within 13mm of power output devices.

Rated maximum Output Power and Clipping: Many people think that as long as the peaks of the output signal voltage stay below the troughs of the ripple voltage, clipping will be avoided. They also calculate the max rated power by assuming that the output voltage can peak just below the ripple's minima. Both are actually incorrect.

They forget that the amplifier has to occupy some of the available voltage range, between the rail and ground. Look at a schematic: Current goes from PSU rail to amplifier then to load then to ground. There is usually at least a transistor's Vce or Vds, and often a low-value resistor, between the power rail and the load.

There is a minimum voltage that must exist across the transistor, for it to operate (Vceo-something, maybe). Certain chipamp datasheets call the minimum voltage between the power and output pins the "clipping voltage", and have plots of it, versus the rail voltage. In my spreadsheet it is called Vclip. It's usually 2 to 5 volts.

It is almost identical to a linear regulator's "dropout voltage". If the signal voltage waveform reaches too high, while at the same time the ripple voltage's waveform sags too low, the ripple voltage will make incursions into the amplifier's "clipping voltage" space, which will effectively gouge chunks out of the output voltage waveform.

Anyway, none of that is "hard" to understand. But it's hard to accurately account for it all unless the actual calculations are performed. So that's one of the main purposes for sharing the spreadsheets I have developed. It would be very inefficient, from the universe's point of view at least, if everyone had to "re-invent the wheel" every time they wanted to make a decision about a power supply.

For all of the math lovers out there, I added the detailed derivation steps for the case where the intervals between charging pulses are less than one-half of the sine signal wavelength (i.e. sine frequencies less than AC mains frequency). I also used MS Word's equation editor to format most of the equations that were previously written with plain text.

If you don't have a compatible version of MS Word, a sample is attached as a jpg, so you can see what you're missing.

I made a minor change, so that the top row can be changed, to make it easy to change the rated max power's percentage of the theoretical (zero-ripple) max power. And I added a few more columns.

Screen images and new version are attached. In the sample screen images, I tweaked the rated vs max power percentages so that the capacitance values came out to more-or-less standard cap values, or combinations of them. The only change I made between the two was to change the rail voltage from 32.7 Volts (for 50 Watts using 22000 uF) to 45 Volts (for 100 Watts using 22000 uF).

I made a minor change, so that the top row can be changed, to make it easy to change the rated max power's percentage of the theoretical (zero-ripple) max power. And I added a few more columns.

Screen images and new version are attached. In the sample screen images, I tweaked the rated vs max power percentages so that the capacitance values came out to more-or-less standard cap values, or combinations of them. The only change I made between the two was to change the rail voltage from 32.7 Volts (for 50 Watts using 22000 uF) to 45 Volts (for 100 Watts using 22000 uF).

So about 200,000 uf is about he max amount to have an effect on power supply stiffness ?